We also use in our construction the classic BCH-codes, see [1]}. We do not employ any specific properties of the construction of the BCH codes. We use only the fact that
\(\forall m >3, t<2^{m-1}\)  exists an explicit construction of a linear code with parameters \([n,k,d]\)  such that codeword length \(n = 2^m-1 \) , the number of checksum bits is \(n-k \le mt\) , and the minimal distance between of the code is \(d\ge 2t+1\) . We also use the fact that the BCH codes can be decoded efficiently (by Berlekamp-Messy algorithm), [2]}.
